Related papers: High Dimensional Robust M-Estimation: Asymptotic V…
Approximate message passing (AMP) type algorithms have been widely used in the signal reconstruction of certain large random linear systems. A key feature of the AMP-type algorithms is that their dynamics can be correctly described by state…
In this work the dynamic compressive sensing (CS) problem of recovering sparse, correlated, time-varying signals from sub-Nyquist, non-adaptive, linear measurements is explored from a Bayesian perspective. While there has been a handful of…
In this paper, we consider the problem of multi-resolution compressed sensing (MR-CS) reconstruction, which has received little attention in the literature. Instead of always reconstructing the signal at the original high resolution (HR),…
The paper studies the problem of distributed parameter estimation in multi-agent networks with exponential family observation statistics. A certainty-equivalence type distributed estimator of the consensus + innovations form is proposed in…
The Approximate Message Passing (AMP) algorithm efficiently reconstructs signals which have been sampled with large i.i.d. sub-Gaussian sensing matrices. Central to AMP is its "state evolution", which guarantees that the difference between…
We propose an estimator of prediction error using an approximate message passing (AMP) algorithm that can be applied to a broad range of sparse penalties. Following Stein's lemma, the estimator of the generalized degrees of freedom, which…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
Since its development, the minimax framework has been one of the corner stones of theoretical statistics, and has contributed to the popularity of many well-known estimators, such as the regularized M-estimators for high-dimensional…
We propose a high-dimensional extension of the heteroscedasticity test proposed in Newey and Powell (1987). Our test is based on expectile regression in the proportional asymptotic regime where n/p \to \delta \in (0,1]. The asymptotic…
Approximate message passing (AMP) methods have gained recent traction in sparse signal recovery. Additional information about the signal, or \emph{side information} (SI), is commonly available and can aid in efficient signal recovery. This…
In this paper we compare and contrast the behavior of the posterior predictive distribution to the risk of the maximum a posteriori estimator for the random features regression model in the overparameterized regime. We will focus on the…
This paper addresses the reconstruction of an unknown signal vector with sublinear sparsity from generalized linear measurements. Generalized approximate message-passing (GAMP) is proposed via state evolution in the sublinear sparsity…
The generalized approximate message passing (GAMP) algorithm under the Bayesian setting shows advantage in recovering under-sampled sparse signals from corrupted observations. Compared to conventional convex optimization methods, it has a…
Transfer learning techniques aim to leverage information from multiple related datasets to enhance prediction quality against a target dataset. Such methods have been adopted in the context of high-dimensional sparse regression, and some…
We develop a message-passing algorithm for noisy matrix completion problems based on matrix factorization. The algorithm is derived by approximating message distributions of belief propagation with Gaussian distributions that share the same…
The aim of this paper is to present a new estimation procedure that can be applied in many statistical frameworks including density and regression and which leads to both robust and optimal (or nearly optimal) estimators. In density…
We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the…
Approximate message passing (AMP) algorithms break a (high-dimensional) statistical problem into parts then repeatedly solve each part in turn, akin to alternating projections. A distinguishing feature is their asymptotic behaviours can be…
A parameter estimation problem is considered, in which dispersed sensors transmit to the statistician partial information regarding their observations. The sensors observe the paths of continuous semimartingales, whose drifts are linear…
Mixed linear regression (MLR) model is among the most exemplary statistical tools for modeling non-linear distributions using a mixture of linear models. When the additive noise in MLR model is Gaussian, Expectation-Maximization (EM)…